Triangular numbers: Difference between revisions
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Thundergnat (talk | contribs) m (→{{header|Raku}}: typo) |
Thundergnat (talk | contribs) m (→{{header|Raku}}: make rounding uniform across root formulas) |
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=={{header|Raku}}== |
=={{header|Raku}}== |
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<syntaxhighlight lang="raku" line>use Math::Root; |
<syntaxhighlight lang="raku" line>use Math::Root; |
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my \ε = FatRat.new: 1, 10**24; |
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sub binomial { [×] ($^n … 0) Z/ 1 .. $^p } |
sub binomial { [×] ($^n … 0) Z/ 1 .. $^p } |
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sub polytopic (Int $r, @range) { @range.map: { binomial $_ + $r - 1, $r } } |
sub polytopic (Int $r, @range) { @range.map: { binomial $_ + $r - 1, $r } } |
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sub triangular-root ($x) { ((8 × $x + 1).&root - 1) / 2 } |
sub triangular-root ($x) { (((8 × $x + 1).&root - 1) / 2).round: ε } |
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sub tetrahedral-root ($x) { |
sub tetrahedral-root ($x) { |
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((3 × $x + (9 × $x² - 1/27).&root).&root(3) + |
((3 × $x + (9 × $x² - 1/27).&root).&root(3) + |
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(3 × $x - (9 × $x² - 1/27).&root).&root(3) - 1).round |
(3 × $x - (9 × $x² - 1/27).&root).&root(3) - 1).round: ε |
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} |
} |
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sub pentatopic-root ($x) { ((5 + 4 × (24 × $x + 1).&root).&root - 3) / 2 } |
sub pentatopic-root ($x) { (((5 + 4 × (24 × $x + 1).&root).&root - 3) / 2).round: ε } |
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sub display (@values) { |
sub display (@values) { |
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} |
} |
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for 2, 'triangular', 3, 'tetrahedral', |
for 2, 'triangular', 3, 'tetrahedral', |
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4, 'pentatopic', 12, '12-simplex' |
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-> $r, $name { |
-> $r, $name { |
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say "\nFirst 30 $name numbers:\n" ~ |
say "\nFirst 30 $name numbers:\n" ~ |
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Roots of 21408696: |
Roots of 21408696: |
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triangular-root: 6543 |
triangular-root: 6543 |
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tetrahedral-root: 503. |
tetrahedral-root: 503.56182697463651404819613 |
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pentatopic-root: 149. |
pentatopic-root: 149.060947375265867484387575 |
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Roots of 26728085384: |
Roots of 26728085384: |
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triangular-root: 231205. |
triangular-root: 231205.405565255836957291031961 |
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tetrahedral-root: 5432 |
tetrahedral-root: 5432 |
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pentatopic-root: 893. |
pentatopic-root: 893.442456751684869888466212 |
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Roots of 14545501785001: |
Roots of 14545501785001: |
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triangular-root: 5393607. |
triangular-root: 5393607.158145172316497304724655 |
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tetrahedral-root: 44355. |
tetrahedral-root: 44355.777384073256052620916903 |
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pentatopic-root: 4321</pre> |
pentatopic-root: 4321</pre> |
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